Finite Element Simulation of Dense Wire Packings

A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.Comment: 17 pages, 7 figures, 1 tabl

Unified Framework for Finite Element Assembly

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain

Analysis of delamination growth with discontinuous finite elements

In this contribution a new finite element is presented for the simulation of delamination growth in thin layered composite materials. The element is based on the solid-like shell element, a volume element that can be used in very thin applications due to a higher order displacement field in thickness direction. The delamination crack is incorporated in this element as a jump of the displacement field by means of the partition of unity method. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples

A general algorithm using finite element method for aerodynamic configurations at low speeds

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem

Evaluation of coupled finite element/meshfree method for a robust full-scale crashworthiness simulation of railway vehicles

The crashworthiness of a railway vehicle relates to its passive safety performance. Due to mesh distortion and difficulty in controlling the hourglass energy, conventional finite element methods face great challenges in crashworthiness simulation of large-scale complex railway vehicle models. Meshfree methods such as element-free Galerkin method offer an alternative approach to overcome those limitations but have proved time-consuming. In this article, a coupled finite element/meshfree method is proposed to study the crashworthiness of railway vehicles. A representative scenario, in which the leading vehicle of a high-speed train impacts to a rigid wall, is simulated with the coupled finite element/element-free Galerkin method in LS-DYNA. We have compared the conventional finite element method and the coupled finite element/element-free Galerkin method with the simulation results of different levels of discretization. Our work showed that coupled finite element/element-free Galerkin method is a suitable alternative of finite element method to handle the nonlinear deformation in full-size railway vehicle crashworthiness simulation. The coupled method can reduce the hourglass energy in finite element simulation, to produce robust simulation

Finite element analysis of aerodynamic heating in three dimensional viscous high speed compressible flow: An assessment

The current capability of the finite element method for solving problems of viscous flow is reviewed. Much work has been directed to the simulation of incompressible flows and the relevant features are described. The methods available for, and the problems associated with, the finite element solution of high speed viscous compressible flows are analyzed. A plan for developing finite element research in this area with experimental support is presented

Finite element modelling and experimental study of oblique soccer ball bounce

In this study, we develop a finite element model to examine the oblique soccer ball bounce. A careful simulation of the interaction between the ball membrane and air pressure in the ball makes the model more realistic than analytical models, and helps us to conduct an accurate study on the effect of different parameters on a bouncing ball. This finite element model includes a surface-based fluid cavity to model the mechanical response between the ball carcass and the internal air of the ball. An experimental set-up was devised to study the bounce of the ball in game-relevant impact conditions. Ball speed, angle, and spin were measured before and after the bounce, as well as ball deformation and the forces during the impact. The finite element model has been validated with three different sets of data, and the results demonstrate that the finite element model reported here is a valuable tool for the study of ball bounce. After validation of the model, the effect of the friction coefficient on soccer ball bounce was studied numerically. Simulation results show that increasing the friction coefficient may result in reversal of the horizontal impact force

Dynamic characterization, monitoring and control of rotating flexible beam-mass structures via piezo-embedded techniques

A variational principle and a finite element discretization technique were used to derive the dynamic equations for a high speed rotating flexible beam-mass system embedded with piezo-electric materials. The dynamic equation thus obtained allows the development of finite element models which accommodate both the original structural element and the piezoelectric element. The solutions of finite element models provide system dynamics needed to design a sensing system. The characterization of gyroscopic effect and damping capacity of smart rotating devices are addressed. Several simulation examples are presented to validate the analytical solution